When Peter tells the story of his ancestor Ulysses S. Griffin, after he finishes his beer first, he places the mug on his head. In the shot of him saying, "Deal," the mug is back on the table. At the next shot, the mug is back on his head.
At the end of the rap sequence in the long-range shot the woman in the blue dress standing next to Peter has brown hair. In the close-up shot following she is blonde.
When Peter is at the United Nations, the delegate from Albania is sitting next to him. Later the Iraqi delegate mentions he's in the third row. Countries in the U.N. are seated alphabetically.
Peter claims to be the President of Petoria, but Petoria does not fit the definition of a Republic. Petoria seems to be an absolute monarchy. If anything, Peter is a King.
Peter fails to get electrocuted when he severs the power mains with his shovel.